Unit 6: Heat and Thermodynamics — Short Questions

Thermal Equilibrium

When two bodies are at the same temperature, the thermal energy (which is related to the kinetic energy of particles) of each body is equal. As a result, there is no driving force for heat transfer between them, and thus they remain in thermal equilibrium.

Example

When we put a metal spoon into a hot cup of coffee
(i) initially, the coffee is hotter than the spoon.
(ii) over time, heat flows from the coffee to the spoon
(iii) eventually, the coffee and spoon reach the same temperature

Thermal equilibrium is achieved at this point, there is no net heat flow between the coffee and the spoon, and they are said to be in thermal equilibrium.

Internal Energy
"The sum of all forms of molecular energies (kinetic and potential) of a substance is termed as its internal energy."
The molecules of an ideal gas are mere points masses which exert no force on one another. So, the internal energy of an ideal gas system is generally the translational K.E. of its molecules.

Dependence on temperature Since the temperature of a system is defined as the average K.E. of its molecules. Thus for an ideal gas system, the internal energy is directly proportional to its
temperature. < 1/2 mv² >= 3/2 k_B T
Where K_B is Boltzmann constant.
Therefore, the rise in temperature of an object represent an increase in internal energy of an ideal gas.

Two common forms of the Second Law of Thermodynamics are:
1. Lord Kelvin Statement:
It is impossible to devise a process which may convert heat taken from a single reservoir entirely into work without leaving any change in the working system.
2. Clausius Statement:
Heat cannot spontaneously flow from a colder body to a hotter body without external work being done on the system.

No, it's not possible to construct a heat engine with 100% efficiency. According to the Second Law of Thermodynamics, some energy will always be lost as heat, making it impossible to achieve perfect efficiency.
The Carnot efficiency limit (η=1- T_c/T_h) suggests a theoretical maximum efficiency, which is always less than 100%. Real-world engines face additional losses, making 100% efficiency unattainable.

Reversible Process
The process which can be retraced by reversing the controlling factors without producing any change in the surrounding is known as reversible process.

Examples i. Slow expansion and compression of the gas.
ii. Liquefaction and Evaporation.
iii. Melting, freezing and boiling etc.

Irreversible process A process which cannot be retraced in the backward direction by reversing the controlling factors is known as irreversible process.

Example (i) Work done against friction is an irreversible process.
(ii) A chemical explosion.
(iii) All engines in practical life.

The adiabatic curve is steeper than the isothermal curve because:
In an adiabatic process, no heat is exchanged, so the gas cools faster as it expands, causing pressure to drop more rapidly.
In an isothermal process, temperature remains constant, so pressure drops more gradually during expansion.

No, a refrigerator does not violate the second law of thermodynamics. While it transfers heat from a colder body to a hotter one, this is done with the help of external work which is done according to the Clausius statement of the second law.

The heat death of the universe refers to a theoretical end state where the universe reaches maximum entropy. In this state, all energy is evenly distributed, no temperature differences exist, and no work or useful energy transformations are possible. It means the universe would be in complete thermodynamics equilibrium. Where due to absence of temperature difference no life or processes could occur.

No, it is not possible for a cyclic reversible heat engine to convert all the absorbed heat into work without rejecting some heat at a lower temperature. This is against second law of thermodynamics Even a reversible (ideal) heat engine must reject a part of the absorbed heat to a sink at lower temperature. No cyclic engine can be 100% efficient.

At high pressure and low temperature, real gases deviate from ideal gas behavior due to:
1. Intermolecular forces: Unlike ideal gases, real gas molecules attract each other at close distances at low temperature, leading to deviate from ideal gas behaviour.
2. Finite molecular volume: Real gas molecules occupy space, so the free volume is less than predicted by the ideal gas law. As ideal gas molecules are assumed to point particles. At high pressure, molecules, are forced to closer together, and their size becomes significant, leading to deviation from ideal gas behaviour.
These effects, neglected in the kinetic theory of ideal gases, become significant under these conditions.

Graphical representation of work The work done by gas on piston can also be calculated by the area under the graph on PV-diagram as shown in Fig.
Area under PV graph = area of ABCD = length × width
W = ΔV × P
Area under PV graph

W = PΔV ----------(1)
∴ For constant pressure

W = PΔV ----------(2)
Comparing Eqs. (1) and (2)
Area under PV – graph = W (work done)
Hence area under PV graph shows the value of work done.

(i) Work done by the gas is taken as positive.
∴ W = Fd cosθ
Here
F = PA
d = Δy
θ = 0°
W = PA Δy cos0° = PA Δy ------------ (1) = PAΔy = PAV ∴ ΔΔy = Δv

(ii) Work done on the gas is taken as negative
W = Fd cosθ
Here F = PA, d = Δy and θ = 180°
W = PA Δy cos(180°) = PAA(– 1) = – PAΔ ∴ ΔV = ΔΔy
W = – PΔV ∴ ΔV = ΔΔy

There is no change in internal energy because the temperature remains constant. It is an isothermal process and during an isothermal process ∆U = 0.

All processes represented in Fig. are cyclic, because in each case system returns to initial state therefore there is no change in internal energy.
Or ∆U = 0

The sum of all form of molecular energy (kinetic and potential) of substance is known as internal energy. It depends upon the temperature. It is state function. The change in internal energy depends upon its initial and final value and is independent of the path (process).

To make use of energy we have to operate an engine which can only be done with the help of a source and a sink at different temperatures since there is no difference of temperature in sea, so we cannot use it.

In real heat engine there are forces of friction between the various parts of engine there are also heat losses. Therefore, part of output of engine is used up in doing work against these dissipative forces, which cause the decrease in its efficiency.

We know the maximum efficiency of reversible engine is
η = (1 - T_c/T_h) × 100
The heat energy takes heat energy from the source convert part of it in mechanical work and rest of it is rejected to sink. Therefore, the output of the engine is always less than input. The efficiency of heat engine is written is:
η = Output/Input × 100
η = ∆W/Q × 100
As ∆W < Q therefore the efficiency is less than 100%.

For working of heat engine two bodies are required one at higher temperature that is call HTR and the other at lower temperature is called LTR or sink. Carnot engine take heat energy from HTR convert part of it in to mechanical work and the remaining part is rejected to sink. For the real heat engine atmosphere is sink hence during it operation it will expel heat to the atmosphere.

Let the heat engine takes heat energy Q₁ from the source and reject Q₂ to sink then heat energy used by engine to convert in mechanical work is Q₁ – Q₂ .
W = Q₁ – Q₂ = 10 – 5 = 5 Joule

The tide in the sea, the blowing of wind, the earthquakes, the radiation of the sun, all are examples due to which entropy is increased.

We know that when Carnot cycle is completed, the net change in internal energy is zero. Hence the net change in entropy is zero.

When temperature of sink is decreased temperature difference increase this will increase the efficiency of heat engine.

1ˢᵗ Law of thermodynamics tells us that heat energy can be converted into equivalent amount of work. 2ⁿᵈ Law tell us the direction of flow of heat and also the amount of heat energy which can be converted into work. It tells us no heat engine is 100% efficient i.e. part of heat supplied must be rejected to a sink.

The process of transformation of energy that occurs within an organism is named as metabolism. From 1ˢᵗ law of thermodynamics, ∆u=Q-W
It tells us that the work done by moving body results in the decrease in internal energy of the body. This decrease is compensated by the energy provided due to the combustion of food.

When gas expands adiabatically; it is internal energy of the gas which is used up in doing work. Thus the internal energy of the system decreases. The temperature being directly related with internal energy drops.

The change in both type depends on their values at final state and independent of the path.
The gravitational P.E has dependence on the gravitational force, whereas internal energy has no such dependence on the field of force.

All natural processes are irreversible in which entropy of system increases. Therefore, change is positive.

First law of thermodynamics expresses the law of conservation of energy by affirming that energy is conserved quantity in isolated systems. It provides a framework to understand how energy transferred and transformed within systems without violating the fundamental principle that energy cannot be created nor destroyed. This alignment underscores the broader applicability and importance of first law in understanding the behaviour of energy in the universe.

Human Metabolism
Human Metabolism also provides an example of energy conservation. Human beings and other animals do work when they walk, run, or move. Work requires energy. Energy is also needed for growth to make new cells and to replace old cells that have died. Energy transforming processes that occur within an organism are named as metabolism. We can apply the first law of thermodynamics.
∆U = Q – W
To an organism of the human body. Work done will result in the decrease in internal energy of the body. Consequently, the body temperature or in other words internal energy is maintained by the food we eat.

In adiabatic expansion, no heat is exchanged with the surrounding. As the gas expands, it does work on the surroundings, due to which internal energy decreases. This leads to decrease in temperature and pressure of the gas.

When a coffee cup is left on the table, it loses heat to the surroundings through convection, conduction and radiation according to second law of thermodynamics, heat flows from coffee to cooler environment (surrounding) until thermal equilibrium is reached.

Weather patterns like wind, rain and storms are results of thermodynamic processes the sun heats the earth unevenly, causing Temperature and pressure differences in the atmosphere. These differences drive winds, cloud formation (condensation of water vapour) and precipitation (release of latent heat), all governed by the laws of thermodynamics.

See Q.1 and Q.4 of theory.

See Q.5 of theory.

See Q.9 of theory.

See Q.15 of theory.

See Q.14 of theory.

See Q.16 of theory.